A hiker leaves her camp and walks 3.5 km in a direction of 55° south of west to the lake. After a short rest at the lake, she hikes 2.7 km in a direction of 16° east of south to the scenic overlook. What is the magnitude of the hiker’s resultant displacement? Round your answer to the nearest tenth.  km What is the direction of the hiker’s resultant displacement? Round your answer to nearest whole degree. °  south of west

Answers

Answer 1

1) Magnitude

Let's take south as positive y-direction and east as positive x-direction. Then we have to resolve both displacements into their respective components:

[tex]d_{1x} = -(3.5 km) cos 55^{\circ}=-2.0 km[/tex]

[tex]d_{1y} = (3.5 km) sin 55^{\circ}=2.87 km[/tex]

[tex]d_{2x} = (2.7 km) sin 16^{\circ}=0.74 km[/tex]

[tex]d_{2y} = (2.7 km) cos 16^{\circ}=2.60 km[/tex]

So, the components of the total displacement are

[tex]d_x = d_{1x}+d_{2x}=-2.0 km +0.74 km=-1.26 km[/tex] east (so, 1.26 km west)

[tex]d_y=d_{1y}+d_{2y}=2.87 km + 2.60 km=5.47 km[/tex] south

So, the magnitude of the resultant displacement is

[tex]d=\sqrt{d_x^2+d_y^2}=\sqrt{(1.26)^2+(5.47)^2}=5.61 km[/tex]


2) Direction

the direction of the hiker's displacement is

[tex]\theta= arctan(\frac{d_y}{d_x})=arctan(\frac{5.47}{1.26})=arctan(4.34)=77.0^{\circ}[/tex] south of west.

Answer 2
Final answer:

The magnitude of the hiker's resultant displacement is 5.8 km south of west.

Explanation:

To find the magnitude of the hiker's resultant displacement, we need to first find the x and y components of the displacement vectors.

Path 1, the hiker walks 3.5 km in a direction of 55° south of west. The x component of this displacement is -3.5 * cos(55°) = -2.503 km, and the y component is -3.5 * sin(55°) = -2.845 km.

Path 2, the hiker walks 2.7 km in a direction of 16° east of south. The x component of this displacement is 2.7 * sin(16°) = 0.732 km, and the y component is -2.7 * cos(16°) = -2.606 km.

The total x component is -2.503 + 0.732 = -1.771 km, and the total y component is -2.845 - 2.606 = -5.451 km. Using the Pythagorean theorem, the magnitude of the resultant displacement is sqrt((-1.771)^2 + (-5.451)^2) = 5.797 km.

The direction can be found using the inverse tangent function, atan((-5.451)/(-1.771)) = 73°. Since the displacement is south of west, the direction is 180 - 73 = 107° south of west.

Learn more about Resultant displacement here:

https://brainly.com/question/29204785

#SPJ3


Related Questions

Which of the following is not a danger associated with hurricanes?
a) droughts
b) inland flooding
c) storm surges
d) tornadoes

Answers

Droughts, because a drought is loss of water access, but a hurricane takes water out of the ocean and rains it down upon landfall.
Final answer:

The correct answer is a) droughts. Hurricanes are typically associated with heavy rain and high winds, which can lead to flooding.

Explanation:

Hurricanes are powerful storms that cause a variety of hazards, including inland flooding, storm surges, and tornadoes.

Inland flooding can occur when the heavy rainfall associated with a hurricane overflows rivers and streams. Storm surges are the rise in sea level that happens when a hurricane's strong winds push water onshore. This can cause significant flooding and damage in coastal areas. Tornadoes can be produced by hurricanes when thunderstorms present within the hurricane system become severe.

However, droughts are not typically a direct result of hurricanes. In fact, the heavy rainfall associated with hurricanes often alleviates drought conditions.

Learn more about Dangers associated with hurricanes here:

https://brainly.com/question/15649592

#SPJ2

Which instrument provides the only means of making nearly continuous measurements of surface conditions over the ocean?

Answers

These instruments are called data buoys.

If the box is a distance 1.81 m from the rear of the truck when the truck starts, how much time elapses before the box falls off the truck?

Answers

If the box is a distance 1.81 m from the rear of the truck when the truck starts, ... Force of Friction = mu_s * Normal Force( M * G) ... The box starts moving! ... Now that the box is moving, the bed of the truck pulls at it with 17.4 ... out how long it will take the box to reach the back of the truck. ... T^2 = 2 * 1.81 / .64
Final answer:

To find the time it takes for the box to fall off the truck, we use the equation of motion and the acceleration of the box relative to the truck. By setting the displacement equal to the distance from the rear of the truck and solving for time, we find that it takes approximately 1.34 seconds for the box to fall off.

Explanation:

To find the time it takes for the box to fall off the truck, we need to first find the acceleration of the box relative to the truck. Given that the truck is accelerating forward at 5.0 m/s² and the crate is accelerating forward at 2.94 m/s², we can subtract these accelerations to find the crate's acceleration relative to the truck, which is -2.06 m/s². Since the box falls off when it reaches a certain distance from the rear of the truck, we can use the equation of motion to find the time it takes to travel that distance.



The equation is:



d = ut + 1/2at²



Where:

d is the displacement or distance traveledu is the initial velocity (0 m/s since the box starts from rest on the truck)t is the time takena is the acceleration

Plugging in the values, we have:



1.81 m = 0 * t + 0.5 * (-2.06) * t²



Simplifying the equation:



1.81 = -1.03t²



Multiplying both sides by -1:



-1.81 = 1.03t²



Dividing both sides by 1.03:



t² = -1.81/1.03



When we take the square root of each side, we obtain:



t = ±√(-1.81/1.03)



The negative value of time implies an event before the start of motion, so we discard it. Therefore, the time it takes for the box to fall off the truck is approximately 1.34 seconds.

Learn more about Time it takes for the box to fall off the truck here:

https://brainly.com/question/33121085

#SPJ2

The component of the ball's velocity whose magnitude is most affected by the collisions is

Answers

The component most affected by the collisions is vertical. The ball's vertical will either decrease or increase due to the collision. If the velocity is high during the collsion the ball's vertical will likely be higher and if the ball's velocity is low the vertical will be as well.

Which of the following statements proves that scientific knowledge changed due to the discovery of the fossil of a hadrosaur in North Dakota?
Hadrosaurs were better runners than earlier thought.
Hadrosaurs had no pattern on their skin, which was not expected.
The length of the hadrosaur was shorter than previously thought.
The muscular structure of the hadrosaur was less developed than expected.

Answers

Hadrosaurs were better runners than earlier thought. The fossilized hadrosaur is well preserved that scientists discovered that its muscle mass is larger and learned that it was even more muscular than what was thought before. Its hindquarters are 25 percent larger than previously thought, meaning they can run up to 28 mph or faster, probably to outrun predators like the T-rex who has a 10 mph running speed. 

They discovered it to be 3 and a half tons in weight and about 40 feet or 12 meters long. The fossil was found in 1999 in North Dakota by a teenager name Lyson, and is now being studied in the world's largest CT scanner operated by Boeing Co. The fossilized dinosaur's name is Dakota. 

An energy pyramid illustrates that energy in the form of _____ is lost to the surroundings as it's passed from one organism to the next

Answers

The answer is metabolic heat.

Organisms from the higher trophic levels consume organisms from the lower trophic level and during that process, energy is lost as metabolic heat. Primary producers (plants) contain the greatest amount of energy originally from the sunlight. The next trophic level belongs to primary consumers that consume primary producers. During consumption, energy is lost. Similarly, secondary consumers eat primary consumers and energy is lost again. The highest trophic level is tertiary consumers that contains the least amount of energy.

A heat pump absorbs heat from the cold outdoors at 3°c and supplies heat to a house at 20°c at a rate of 30,000 kj/h. if the power consumed by the heat pump is 3 kw, the coefficient of performance of the heat pump is

Answers

Final answer:

The coefficient of performance (COP) of a heat pump is a measure of its effectiveness and is defined as the ratio of the heat transfer into the warm space to the work input required by the heat pump.

Explanation:

The coefficient of performance (COP) of a heat pump is a measure of its effectiveness and is defined as the ratio of the heat transfer (Qh) into the warm space to the work input (W) required by the heat pump. Mathematically, COP = Qh/W.

In this case, the heat pump absorbs heat from the cold outdoors at 3°C and supplies heat to a house at 20°C. The rate of heat transfer is given as 30,000 kJ/h and the power consumed is 3 kW.

To find the COP, we need to convert the rate of heat transfer and power consumed to the same units. Since 1 W = 1 J/s and 1 kJ = 1000 J, we have Qh = 30,000 kJ/h x 1000 J/kJ / 3600 s/h = 8333.33 J/s and W = 3kW x 1000 J/W = 3000 J/s.

Substituting these values into the formula, we get COP = 8333.33 J/s / 3000 J/s = 2.78.

Learn more about coefficient of performance here:

https://brainly.com/question/30902201

#SPJ12

Which of the following takes place in the combustion chamber of a gas turbine engine?

Answers

In the combustion chamber of a gas turbine engine the mixture of fuel oil and compressed air is ignited. The combustion chamber is responsible for supplying the energy which drives the system. For a turbine, the combustion chamber operates with periodical combustion and the space, where the combustion takes place is closed on the exhaust side leading to the actual turbine.

The sign has a mass of 100 kg with center of mass at g. determine the x, y, z components of reaction at the ball-and-socket joint a and the tension in wires bc and bd.

Answers

Final answer:

The problem is about finding the reaction components at a ball-and-socket joint and the tension in wires supporting a sign. You can do this by breaking the forces and moments into their x,y,z components, setting up force balance and moment balance equations, and solving for the unknowns.

Explanation:

This problem pertains to static equilibrium, where both the sum of forces and the sum of torques are zero. To begin, let's establish a coordinate system where the ball-and-socket joint 'a' is considered the origin.

Assuming the tension in the wires is T and the angles of the wires to the x, y, z axes are known, you can break the tensions into their respective components using trigonometric principles. Let's consider Tbc and Tbd to be the tensions in the strings.

For the x-component we would sum up the forces in the x-direction and set it equal to zero. This can be represented as ∑Fx = Tbc,x + Tbd,x=0

The same goes for the y and z components with the z component taking into account the force due to gravity on the sign. Hence, ∑Fy = Tbc,y + Tbd,y=0 and ∑Fz = Tbc,z + Tbd,z - weight of the sign = 0. Here, the weight of the sign is 100kg*9.81m/s2

By balancing torques about each axis, you can find the tensions in the strings. The tension force should be the same in each wire if they make the same angles with the axes and are of equal length.

Learn more about Mech Physics here:

https://brainly.com/question/34644538

#SPJ12

Final answer:

This problem in Physics requires setting up equilibrium equations based on the given mass and calculating forces at the ball-and-socket joint and cable pressures.

Explanation:

The subject of this question falls under the branch of

Physics

referred to as statics, specifically the study of systems in equilibrium. Equilibrium implies that an object is neither accelerating nor rotating, meaning the sum of all forces and the sum of all torques acting on the object must both be zero. The 'x', 'y' and 'z' components referred to are likely part of a coordinate system used to describe the forces at work on the sign.

To determine these, one would need to set up equilibrium equations based on the known details about the system, which could include the known weight (provided by the mass of the sign and gravity), any relevant distances for calculating torques, and any other forces present such as tension in wires. The process of solving this system of equations would then yield the desired reaction components at the ball-and-socket joint and the tensions in the wires.

Learn more about Statics here:

https://brainly.com/question/33327144

#SPJ2

What force is needed to accelerate a 55kg shopping cart 2.0m/s to the second power?

Answers

A 55kg shopping cart would need 110N of force in order to accelerate it at 2.0m/s to the second power. This is because the net force equals mass times acceleration.

How will sunlight most likely affect a black shirt on a hot summer day?

Answers

The temperature of the shirt will increase because all wavelengths of light are absorbed by the shirt.

The sunlight is absorbed more on to the black color and no color is reflected back therefore, heat energy is released by the black color and make more hot.

What is light reflection?

When a light ray is incident on a transparent or translucent material, the light ray will return back after some fraction of it is absorbed on the material and the light ray travel in the straight direction from the material make it gleams.

White light absorbs all colors and reflects back all colors. Thus, the mixing of all reflected colors make the material white in color. A black light absorbs all colors and reflect no color.

The absorbed light energy in the black body is released as heat energy instead. This make the black colored material more hotter than other colors. Hence, a black shirt is most affected by sunlight.

To find more on reflection, refer here:

https://brainly.com/question/28969632

#SPJ2

in texas the speed limited in a/an is 30 mph

Answers

In Texas, the speed limit in urban districts is generally set at 30 mph unless otherwise posted. This means that unless there are signs indicating a different speed limit, drivers are expected to adhere to a maximum speed of 30 miles per hour when traveling through urban areas. Therefore, the correct answer is A. 30 mph.

The rationale behind setting a default speed limit for urban districts is to promote safety for both motorists and pedestrians. Urban areas typically have higher population densities, increased pedestrian activity, and more complex traffic patterns compared to rural or suburban areas. As a result, lower speed limits help reduce the risk of accidents, particularly those involving pedestrians and cyclists.

By setting a default speed limit of 30 mph in urban districts, Texas law aims to create safer environments for all road users. However, it's essential for drivers to remain vigilant and observant of posted speed limit signs, as speed limits may vary depending on factors such as road conditions, proximity to schools or residential areas, and construction zones.

Overall, the default speed limit of 30 mph in urban districts reflects a balance between ensuring efficient traffic flow and prioritizing the safety of all individuals on the road. Therefore, the correct answer is A. 30 mph.

The complete question is:

In Texas, the speed limit in urban districts is _______ unless otherwise posted.

A. 30 mph

B. 50 mph

C. 40 mph

D. 25 mph

For an increase in the bulk modulus of a material but without any change in the density, what happens to the speed of sound in that material?

Answers

The speed of sound, c, is given by the Newton-Laplace formula
[tex]c = \sqrt{ \frac{K}{\rho} } [/tex]
where
K = bulk modulus
ρ =  density

Because the density is constant, the speed of sound is proportional to the square root of the bulk modulus.

Therefore when the bulk modulus increases, the speed of sound increases by the square root of the bulk modulus.

For example, if K is doubled, then
[tex]c = \sqrt{2K} = \sqrt{2} \sqrt{K} [/tex]

Answer:
If the bulk modulus increases by a factor of n, then c increases by a factor of √n.

Final answer:

The speed of sound within a substance depends on the bulk modulus and density of the material. An increase in bulk modulus, with density remaining constant, would increase the speed of sound within the material, given that the speed of sound is proportional to the square root of the bulk modulus.

Explanation:

The speed of sound within a substance is primarily determined by two physical properties of the material, namely the bulk modulus and density. The bulk modulus measures a substance’s resistance to uniform compression. The formula used to calculate the speed of sound within a substance is v = sqrt(B/p), where 'v' represents the speed of sound, 'B' signifies the bulk modulus of the material, and 'p' indicates the density of the material.

As such, if the bulk modulus of a material were to increase while the density remained constant, the speed of sound within that material would also increase because the speed of sound is directly proportional to the square root of the bulk modulus. For instance, since solids and liquids are generally more rigid (i.e., have higher bulk modulus values) than gases, the speed of sound tends to be greater in these media than in gases, assuming density remains constant.

Learn more about Speed of Sound here:

https://brainly.com/question/35989321

#SPJ11

A spring that has a spring constant of 1400 N/m is stretched to a length of 2.5 m. If the normal length of the spring is 1.0 m, how much elastic potential energy is stored in the spring? 700 J 1050 J 1575 J 4375 J

Answers

The answer is 1575, I just took the Review.

The manometer shown in fig. 2 contains water and kerosene. with both tubes open to the atmosphere, the free-surface elevations differ by h = 20.0 mm. determine the elevation difference when a pressure of 98.0 pa (gage) is applied to the right tube. (hint: when the gage pressure is applied to the right tube, the water in the right tube is displaced downward by the same distance that the kerosene in the left tube is displaced upward)

Answers

The elevation difference is 55.3 mm when a pressure of 98.0 Pa (gage) is applied to the right tube of the manometer, displacing water downward and kerosene upward.

When a pressure of 98.0 Pa (gage) is applied to the right tube of the manometer, the water in the right tube is displaced downward by the same distance that the kerosene in the left tube is displaced upward, maintaining equilibrium.

To find the elevation difference, we can use the hydrostatic pressure formula:

P = ρgh

Where:

P = pressure difference (98.0 Pa in this case)

ρ = density of the fluid (for water, ρ_water ≈ 1000 kg/m³, for kerosene, ρ_kerosene ≈ 820 kg/m³)

g = acceleration due to gravity (approximately 9.81 m/s²)

h = elevation difference

Since the water and kerosene columns have opposite elevation changes, we can write:

98.0 Pa = (ρ_water * g * h) - (ρ_kerosene * g * h)

Now, solve for h:

98.0 Pa = (1000 kg/m³ * 9.81 m/s² * h) - (820 kg/m³ * 9.81 m/s² * h)

98.0 Pa = (9810 h) - (8034 h)

98.0 Pa = 1776 h

h = 98.0 Pa / 1776 = 0.0553 meters = 55.3 mm

So, when a pressure of 98.0 Pa (gage) is applied to the right tube, the elevation difference between the two free surfaces in the manometer is 55.3 mm.

For more question on manometer visit:

https://brainly.com/question/17209103

#SPJ11

Suppose a supernova occurs in a star that initially had 10 solar masses. why would the likely end result not be a black hole?

Answers

When a supernova occurs, a very large portion of the stars' mass is lost. In order to create a black hole, at least 30 solar masses is needed, so starting with 10 and losing a large portion of that mass is nowhere near enough to create a black hole. The end result would be a Neutron star.
Final answer:

A star with an initial mass of 10 solar masses will likely form a neutron star instead of a black hole after a supernova due to the mutual repulsion between densely packed neutrons that can support the core against its own gravitational weight.

Explanation:

Given a star with initial 10 solar masses that ends its life in a supernova explosion, it is more likely to form a neutron star rather than a black hole. Most stars end their life as white dwarfs or neutron stars. In the case of a very massive star, if the core's remaining mass is more than about three times that of the Sun, it may collapse into a black hole. However, if the mass is less than about three solar masses, the mutual repulsion between densely packed neutrons can support the core against its own weight, preventing it from becoming a black hole.

Learn more about Supernova here:

https://brainly.com/question/33455867

#SPJ11

A uniform disk is constrained to rotate about an axis passing through its center and perpendicular to the plane of the disk. if the disk starts from rest and is then brought in contact with a spinning rubber wheel, we observe that the disk gradually begins to rotate too. if after 22 s of contact with this spinning rubber wheel, the disk has an angular velocity of 3.0 rad/s, find the average angular acceleration that the disk experiences. (assume the positive direction is in the initial direction of rotation of the disk. indicate the direction with the sign of your answer.)

Answers

? ? ? ? ? ? ? ? ? ? ?

It is friction that provides the force for a car to accelerate, so for high-performance cars the factor that limits acceleration isn't the engine; it's the tires. you may want to review ( pages 138 - 142) . part a for typical rubber-on-concrete friction, what is the shortest time in which a car could accelerate from 0 to 60 mph? suppose that μs=1.00 and μk=0.80.

Answers

The shortest time in which a car could accelerate from 0 mph to 60 mph is [tex]13.7s[/tex].

Further explanation:

The opposite force acting on the body is known as frictional force. It always acts in the opposite direction of motion of body.

Concept used:

The force applied to a body to keep it at rest is known as the static friction force. It always acts opposite to the direction of motion of body. It is defined as the product of coefficient of friction and the normal force acting on the body.

The expression for the normal reaction of the body is given as.

[tex]N = mg[/tex]  

The expression for the net force is given as.

[tex]{F_{net}} = ma[/tex]                                 …… (1)

The expression for the static friction is given as.

[tex]{F_s} = {\mu _s}N[/tex]

The expression for the balanced forces is given as.

[tex]{F_{net}} = {F_s} - {F_r}[/tex]

 

Substitute[tex]{\mu _s}N[/tex] for [tex]{F_s}[/tex] and  for[tex]{F_r}[/tex] in the above expression.

[tex]\begin{aligned}{F_{net}}&={\mu _s}N-{\mu _r}N\\&= \left( {{\mu _s} - {\mu _r}} \right)N \\ \end{aligned}[/tex]

Substitute [tex]mg[/tex] for [tex]N[/tex] in above expression.

[tex]{F_{net}}=\left({{\mu _s}-{\mu _r}}\right)\left( {mg}\right)[/tex]       …… (2)

Compare equation (1) and (2) we get.

[tex]a=g\left({{\mu _s}-{\mu _r}}\right)[/tex]                              …… (3)

Here, [tex]a[/tex] is the acceleration of the body, g is the acceleration due to gravity, [tex]{\mu _s}[/tex] is the coefficient of static friction and  is the coefficient of reactive force.

The expression for the first equation of motion is given as.

[tex]v = u + at[/tex]      

                             

Rearrange the above expression for time is given as.

[tex]\fbox{\begin\\t = \dfrac{{\left( {v - u} \right)}}{a}\end{minispace}}[/tex]                              …… (4)

Here, [tex]v[/tex] is the final velocity, [tex]u[/tex] is the initial velocity and [tex]t[/tex] is the time.

Substitute [tex]1[/tex] for [tex]{\mu _s}[/tex], [tex]0.8[/tex] for[tex]{\mu _r}[/tex] and [tex]9.8\,{\text{m/}}{{\text{s}}^{\text{2}}}[/tex] for [tex]g[/tex] in equation (3).

[tex]\begin{aligned}a&=\left( {9.8\,{\text{m/}}{{\text{s}}^{\text{2}}}}\right)\left( {1 - 0.8}\right)\\&=1.96\,{\text{m/}}{{\text{s}}^{\text{2}}} \\ \end{aligned}[/tex]

 

Substitute [tex]0\,{\text{mph}}[/tex] for [tex]u[/tex], [tex]60\,{\text{mph}}[/tex] for [tex]v[/tex] and [tex]1.96\,{\text{m/}}{{\text{s}}^{\text{2}}}[/tex] for [tex]a[/tex] in equation (4).

[tex]\begin{aligned}t&=\frac{{\left( {60\,{\text{mph}}-0\,{\text{mph}}}\right)}}{{1.96\,{\text{m/}}{{\text{s}}^{\text{2}}}}}\\&=\frac{{60\,{\text{mph}}\left( {\frac{{0.447\,{\text{m/s}}}}{{1\,{\text{mph}}}}} \right)}}{{1.96\,{\text{m/}}{{\text{s}}^{\text{2}}}}}\\&= 13.7\,{\text{s}} \\ \end{aligned}[/tex]

 

Thus, the time required to accelerate a car is [tex]\fbox{\begin\\13.7\, {\text{s}}\end{minispace}}[/tex].

Learn more:

1.  Conservation of momentum https://brainly.com/question/9484203.

2.  Motion under friction https://brainly.com/question/7031524.

3. Net force on the body https://brainly.com/question/4033012.

Answer Details:

Grade: College

Subject: Physics

Chapter: Kinematics

Keywords:

Force, friction, Acceleration, acceleration due to gravity, normal, weight, mass, motion, sliding, sled, hill, inclined, plane, coefficient of friction, angle of inclination, 13.68 s, 13.69 s.  

Final Answer:

So, under ideal conditions with the assumption of maximum static friction being available throughout the acceleration, the shortest time in which a typical car could accelerate from 0 to 60 mph on rubber-on-concrete would be approximately 2.734 seconds.

Explanation:

To solve this problem, we need to understand how the force of friction allows a car to accelerate and then apply the equations of motion to determine the shortest time it would take for the car to accelerate from 0 to 60 miles per hour (mph).

First, we need to define our variables and constants:
- The static friction coefficient between rubber and concrete, μs, which is 1.00. This is the factor that will limit our acceleration since it represents the maximum frictional force that can be exerted before sliding begins.
- The acceleration due to gravity, g, which is 9.81 m/s^2.
- The initial speed of the car, 0 mph, which needs to be converted to meters per second (m/s).
- The final speed of the car, 60 mph, which also needs to be converted to meters per second.

The force of static friction (f_friction) responsible for the acceleration can be calculated by multiplying the static friction coefficient (μs) with the normal force (N). The normal force, in this case, is equal to the weight of the car, which is the mass (m) times the acceleration due to gravity (g). Since we are looking for the highest possible acceleration, we can assume that the force of static friction is at its maximum value.

f_friction = μs * m * g

However, we don't need to know the mass of the car because it will cancel out in the equation of motion. The maximum possible acceleration (a_max) happens when the force of static friction is at its highest, and it can be calculated using:

a_max = f_friction / m = μs * g

Now we have the maximum possible acceleration the tires can provide on concrete, which is:

a_max = 1.00 * 9.81 m/s^2
a_max = 9.81 m/s^2

Next, let's convert the final velocity from mph to m/s:

v_final(mph) = 60 mph
v_final(m/s) = v_final(mph) * 0.44704 (conversion factor from mph to m/s)
v_final(m/s) = 60 * 0.44704
v_final(m/s) ≈ 26.8224 m/s

With the initial velocity (v_initial) being 0 m/s (since we start from rest), we can use one of the kinematic equations to find the time (t):

v_final = v_initial + a_max * t
26.8224 m/s = 0 m/s + 9.81 m/s^2 * t

Solving for t, we get:

t = v_final / a_max
t ≈ 26.8224 m/s / 9.81 m/s^2

t ≈ 2.734 seconds

So, under ideal conditions with the assumption of maximum static friction being available throughout the acceleration, the shortest time in which a typical car could accelerate from 0 to 60 mph on rubber-on-concrete would be approximately 2.734 seconds.

A force of 660 n stretches a certain spring a distance of 0.300 m. what is the potential energy of the spring when a 70.0 kg mass hangs vertically from it?

Answers

A force of 660 n stretches a certain spring a distance of 0.300 m. what is the potential energy of the spring when a 70.0 kg mass hangs vertically from it?

A child sets off the firecracker at a distance of 100 m from the family house. what is the sound intensity β100 at the house?

Answers

To solve this problem, we use the formula:

I100 / I1 = [P / 4π(100m)^2] / [P / 4π(1m)^2]

I100 / I1 = 1 / 100^2

I100 / I1 = 10^-4

 

Therefore the change in intensity from 1m to 100m in decibels is:

B100 – B1 = 10 log(10^-4) dB = -40 dB

 

So the intensity at 100m is calculated as:

B100 = B1 – 40 dB = 140 dB – 40 dB = 100 dB

 

Answer:

100 dB

The intensity of the sound produced due to the firecracker at the distance of [tex]100\text{ m}[/tex] is [tex]\fbox{\begin\\100\text{ dB}\end{minispace}}[/tex].

Further Explanation:

The vibration, produced in the medium, which travels as an wave of pressure or density through a medium is known as sound. The sound is a longitudinal wave and it requires a medium for its propagation.  

Given:

The distance between the place where firecracker is set off by a child and the family house is [tex]100\text{ m}[/tex].  

The intensity of the sound produced by the firecracker at the distance [tex]1\text{ m}[/tex] is[tex]140\text{ dB}[/tex].

Concept:

The intensity of the sound wave is defined as the power carried by the sound waves in the direction perpendicular to the direction of propagation per unit time.

The intensity of the sound wave is:

[tex]\fbox{\begin\\I=\dfrac{P}{4\pi r^2}\end{minispace}}[/tex]                                                        ...... (1)

Here, [tex]I[/tex] is the intesnity of the sound wave, [tex]P[/tex] is the power carried by the sound wave and [tex]r[/tex] is the distance between source and the listener.

The intensity of the sound in decible at the house is:

[tex]\fbox{\begin\\\beta _{100}=\beta _{1}+10\log \dfrac{I_{100}}{I_{1}}\end{minispace}}[/tex] ...... (2)

Here, [tex]\beta _{100}[/tex] is the intensity of the sound at the distance of [tex]100\text{ m}[/tex], [tex]\beta _{1}[/tex] is the intensity of sound produced by the firecracker at the distance of [tex]1\text{ m}[/tex], [tex]I_{100}[/tex] is the intensity of sound produced by firecracker at [tex]100\text{ m}[/tex] and [tex]I_{1}[/tex] is the intensity of sound produced by firecracker at [tex]1\text{ m}[/tex].

The ratio of the intensity of sound at distance [tex]100\text{ m}[/tex] and [tex]1\text{ m}[/tex] is:

[tex]\fbox{\begin\\\dfrac{{{I_{100}}}}{{{I_1}}}=\frac{{r_1^2}}{{r_2^2}}\end{minispace}}[/tex]                                                                                     …… (3)

Calculation:

Substitute the values in equation (3).

[tex]\begin{aligned}\frac{{{I_{100}}}}{{{I_1}}}&=\frac{{{{\left( 1 \right)}^2}}}{{{{\left( {100} \right)}^2}}}\\&={10^{ - 4}}\\\end{aligned}[/tex]

Substitute the values in equation (2).

[tex]\begin{aligned}{\beta _{100}}&=140\,{\text{dB}} - 40\,{\text{dB}} \\&=100\,{\text{dB}}\\\end{aligned}[/tex].

Thus, the intensity of the sound produced due to the firecracker at the distance of [tex]100\text{ m}[/tex] is [tex]\fbox{\begin\\100\text{ dB}\end{minispace}}[/tex]

Learn more:

1.  The motion of a body under friction brainly.com/question/4033012

2.  A ball falling under the acceleration due to gravity brainly.com/question/10934170

3. Conservation of energy brainly.com/question/3943029

Answer Details:

Grade: College

Subject: Physics

Chapter: Waves and Oscillation

Keywords:

Intensity of sound, sound waves, vibration, firecracker, power carried by sound waves, 100db, 100 dB, 100dB, 100 m, bursting of firecrackers, sound inside the house, 140 db, 140 dB.

The board sandwiched between two other boards shown below weighs 87.5 n. if the coefficient of friction between the boards is 0.622, what must be the magnitude of the compression forces (assume horizontal) acting on both sides of the center board to keep it from slipping?

Answers

Refer to the diagram shown below.

W = 87.5 N, the weight of the sandwiched board.
μ = 0.622, the static coefficient of friction.

From the free body diagram of the sandwiched board, obtain
2μF = W
F = W/(2μ) = 87.5/(2*0.622) = 70.34 N

Answer: 70.34 N

The compression forces acting on both sides of the center board = 70.338 N

Further explanation

The force acting on a system with static equilibrium is 0

[tex] \large {\boxed {\bold {\sum F = 0}} [/tex]

(forces acting as translational motion only, not including rotational forces)

[tex] \displaystyle \sum F_x = 0 \\\\\ sum F_y = 0 [/tex]

For objects undergoing rotation, the equilibrium must be met

[tex] \large {\boxed {\bold {\sum \tau = 0}} [/tex]

The force acting on the touchpad between the two fields is called the normal force  (N)

While the frictional force arises because of 2 objects that come into direct contact, especially when there is motion between two objects that are in direct contact.

There are 2 friction forces

static friction: fs = us.N kinetic friction: fk = uk .N

The board sandwiched between two other boards will not fall if

a downward force = an upward force

or ΣFy = 0 (idle / equilibrium)

so that

A downward force = weight of the board sandwiched = 87.5 N

An upward force = arises from two static friction forces namely: us.N (N =  reaction force of the compression forces=F) ---> us.F

then the force that works can be stated:

EFy = 0

W = 2fs

W = 2 (us.F)

87.5 N = 2 (0.622. F)

F = 70,338 N

Learn more

law of motion

brainly.com/question/75210

displacement of a skateboarder

brainly.com/question/1581159

The distance of the elevator

brainly.com/question/8729508

Two waves of equal magnitude but opposite phase interfere with one another to cause the waves to disappear. This is caused by:

each wave canceling the other out, causing the waves to disappear completely

refraction of waves multiplying each other's amplitude with the effect of canceling each other out

the Conner effect

destructive interference giving the effect of making the waves disappear, but each will travel on its way

Answers

Destructive Interference. This gives the effect of making the two waves disappear at the moment they meet. After the 2 waves cancel each other at the monent when they overlap, the waves continue in the same direction and magnitude as they were originally.

PLZ HELP: Which food items would be appropriate for a spacecraft? Check all that apply. A< brownie, B< dry salt and pepper, C

Answers

B. where is the rest of C?
My answer is B

A 1490-kilogram truck moving with a speed of 27.0 m/s runs into the rear end of a 1280-kilogram stationary car. if the collision is completely inelastic, how much kinetic energy is lost in the collision?

Answers

Hi I can help follow me and I will

The loss in kinetic energy in an inelastic collision is equal to 251104 J.

What is law of conservation of momentum?

According to the law of conservation of linear momentum, the sum of the momentum before and after an inelastic collision must be equal.

m₁u₁ + m₂ u₂ =   m₁ v₁ + m₂ v₂

where m₁ and m₂ is the mass of the collided bodies, u₁ & u₂ are their initial speed while v₁ & v₂ is their final speed.

Given the initial velocity of the truck is v₁ = 27 m/s and the other car is at rest, u₂ = 0 m/s.

The mass of the truck, m₁ = 1490 Kg

The mass of the stationary car, m₂ = 1280 Kg

From the law of conservation of momentum, find the final speed after a collision:

m₁ u₁ + m₂ u₂ = (m₁ + m₂)v'

1490 × 27 + 1280 ×0 = (1490 + 1280) v'

v' = 14.52 m/s

The loss in the kinetic energy = [tex]=\frac{1}{2} mv_1^2-\frac{1}{2} (m_1+m_2)^2v^'^2[/tex]

[tex]==\frac{1}{2} \times 1490\times(27)^2-\frac{1}{2} (2770)^2(14.52)^2[/tex]

[tex]= 543105 -292000\\=251104 J[/tex]

Therefore, the loss in the kinetic energy in the collision is equal to 251104 J.

Learn more about the law of conservation of linear momentum, here:

brainly.com/question/17140635

#SPJ5

What would most likely happen if the power lines in a pretroleum power plant were broken

Answers

If a power lines in a petroleum power plant were broken CUSTOMERS WOULD NOT RECEIVE ELECTRICITY.
Power lines are used in electrical power transmission to transmit electrical energy across large distances. When these lines are broken, the generating plant will not be able to send electricity across to the consumers.

A train accelerates from its metropolitan cruising speed of 22 m/s to its countryside cruising speed of 32 m/s. If it takes the train 142 seconds to do this, what is its acceleration?

10 m/s2
14.2 m/s2
4.4 m/s2
0.07 m/s2

Answers

Since it mentions in the problem that it took 142 seconds for 22 m/s to become 32 m/s, one should multiply 142 by the answer choices. This will determine how many m/s2 was needed to get the change in speed. Then it will be added to the 22m/s to see what is closest to 32 m/s. 

142*10 = 1420+22 = 1442. Too much.
142*14.2 = 2016.4+22 = 2038.4. Too much. Even rounding doesn't do it justice, of course.
142*4.4 = 624.8+22 = 646.8. Too much. Rounding won't work here, either.
142*0.07 = 9.94+22 = 31.94. This is the closest out of all of them, and when rounded it comes up as 32. 

So, the answer would be 0.07 m/s2.

Answer:

Acceleration of the train is 0.07 m/s²            

Explanation:

Initial speed of the train, u = 22 m/s

Final speed of the train, v = 32 m/s

Time taken by the train to do the process is 142 seconds

We have to find the acceleration of the train. It is given by the rate of change of speed of the train i.e.

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]a=\dfrac{32\ m/s-22\ m/s}{142\ s}[/tex]

[tex]a=0.07\ m/s^2[/tex]

So, the acceleration of the car is 0.07 m/s². Hence, the correct option is (d) 0.07 m/s²

A ball is thrown horizontally from a cliff at a speed of 10 m/s. you predict that its speed 1 s later will be slightly greater than 14 m/s. your friend says it will be 10 m/s. show who is correct.

Answers

The horizontal component of speed remains constant at 10 m/s.
After 1 s, a vertical component of speed = gt = 9.8(1) = 9.8 m/s is added to the horizontal speed.
The size of the total speed of the ball after 1 s = √(10²+9.8²) = √196.04 ≈ 14.0 m/s <=
You are correct.

Answer:

Speed is slightly greater than 14 m/s.          

Explanation:

The ball will under go projectile motion. The horizontal velocity remains constant while there would be increase in vertical velocity due to acceleration due to gravity in downward direction.

Using first equation of motion, after 1 s, vertical velocity will be:

v = u +at

v=0+(9.8 m/s²)(1 s) = 9.8 m/s

Horizontal velocity = 10 m/s

Net velocity:

[tex]V= \sqrt{(9.8)^2+(10)^2}=\sqrt{196.04}=14.001 m/s[/tex]

Speed is slightly greater than 14 m/s.

Which statement best describes a commission system? A legislative body hires a leader to oversee city departments. An elected leader and an elected legislative body share responsibility. A leader oversees city departments, and a legislative body has limited power. A legislative body oversees city departments directly.

Answers

Answer;

A legislative body oversees city departments directly.

Explanation;

City commission government is a form of local government in the United States. In a city commission government, voters elect a small commission, typically of five to seven members, on a plurality-at-large voting basis.

The commissioners constitute the legislative body of the city and, as a group, are responsible for taxation, appropriations, ordinances, and other general functions.

Answer:

a legislative body oversees city departments directly

Explanation:

Alcohols are organic compounds that contain a. carbon and oxygen only. c. carbon, oxygen, and hydrogen. b. carbon and hydrogen only. d. carbon, nitrogen, and hydrogen.

Answers

C
I think that it is  carbon, oxygen, and hydrogen

Answer: Option (c) is the correct answer.

Explanation:

Compounds which contain carbon and hydrogen atoms are known as organic compounds.

As general chemical formula of alcohols is R-OH, where R = any alkyl or aryl group.

For example, [tex]CH_{2}CH_{2}OH[/tex] is known as ethanol and it is an alcohol as it contains the functional group "-OH".

So, alcohols contains elements carbon, hydrogen and oxygen.

Thus, we can conclude that alcohols are organic compounds that contain carbon, oxygen, and hydrogen.

you toss a coin into a wishing well full of liquid denser than the coin. witch of the following could be true? the coin will

Answers

The coin will float because the liquid is denser than it
Other Questions
This poem:1 Confusion2 My head is spinning like a tornado3 I cannot hear myself think4 Why is it so loud in here5 I must get away from this place6 ChaosThe phrase "my head is spinning like a tornado" shows that the writer --A wants to leaveB is feeling extremely angryC cannot focusD likes the feeling of spinning around the no - Nothing party became successful for a brief period because which weights would you use on a single thread to create a 6.86N force An unknown cell is placed in an unknown solution. the cell ends up swelling and then lysing, explodes. which type of solution was this cell placed in? draw your own example of this below. Is the speaker telling about recent events or ones that happened many years ago? What government policies hurt the economy following the war When factor is change when a pure element becomes an ion? 1. 1 5/8 divided by - 1 3/52. -5 1/3 divided by 2 3/4 which of the following words could be used to describe a skillful guitar player?A. adroitB. pliableC. ineptD. restrained Divide. (3 3/4)(2 1/2) Enter your answer as a mixed number, in simplified form, in the box. The endocrine gland that is often called the "master gland" because it affects the output of the other endocrine glands is the ____________ glanda. pituitaryb. pinealc. thyroidd. adrenal In the united states, the army, air force, navy, marines, and coast guard fulfill a purpose of government. what is it? Whats the property shown for this problem? ||Associative||Commutative||Opposite||-2.2 + (-3.7 + (-1.4)) = (-2.2 + (-3.7)) + (-1.4) Which groups belief in one God excused it from worshiping Roman gods? Find the median: 95, 103, 98, 62, 31, 15, 82 _____, the decision to arrest someone or even to ignore a matter, is a routine part of police work. Write the expressions without using log. Can someone please help with this?(i) log m^2 n =?(ii) log (m/n^3)=? Brad and Wes are building a tree house. They cut a 12 and a half foot piece of wood into 5 of the same length pieces?How long is each piece of wood? Swelling occurs around the area of a scratch is what immune response?A. Innate responseB. Adaptive response Source: Robin Hood and the Scotchman. The Robin Hood Garlands and Ballads. Ed. John Mathew Gutch, William Hone, Francis Douce, and Edward Francis Rimbault. London: John Russell Smith and Joseph Lilly, 1750. 392-93. Google Books. Web. 24 June 2011. What is the structure of this poem? ballad free verse sonnet blank verse Steam Workshop Downloader